Numerical analysis for the two-dimensional Fisher–Kolmogorov–Petrovski–Piskunov equation with mixed boundary condition

In this paper, a finite difference scheme is presented for the initial-boundary value problem for the two-dimensional nonlinear Fisher–Kolmogorov–Petrovski–Piskunov (Fisher–KPP) equation with mixed boundary conditions. Using Energy functional, stability of the suggested scheme is achieved. Unique solvability of the difference solutions is proved. Furthermore, the second-order convergence in the discrete H1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^{1}$$\end{document}-norm is established. Finally, two numerical experiments are reported to validate the theoretical analysis.